Situation Calculus Meets Description Logics

For more than six years, the groups of Franz Baader and Gerhard Lakemeyer have collaborated in the area of decidable verification of Golog programs. Golog is an action programming language, whose semantics is based on the Situation Calculus, a variant of full first-order logic. In order to achieve decidability, the expressiveness of the base logic had to be restricted, and using a Description Logic was a natural choice. In this chapter, we highlight some of the main results and insights obtained during our collaboration.

[1]  Phokion G. Kolaitis,et al.  On the Decision Problem for Two-Variable First-Order Logic , 1997, Bulletin of Symbolic Logic.

[2]  Franz Baader,et al.  Using Causal Relationships to Deal with the Ramification Problem in Action Formalisms Based on Description Logics , 2010, LPAR.

[3]  Franz Baader,et al.  Integrating Description Logics and Action Formalisms: First Results , 2005, Description Logics.

[4]  Jens Claßen,et al.  Decidable Verification of Decision-Theoretic Golog , 2017, FroCoS.

[5]  Stephan Schulz,et al.  System Description: E 1.8 , 2013, LPAR.

[6]  Gerhard Lakemeyer,et al.  Exploring the Boundaries of Decidable Verification of Non-Terminating Golog Programs , 2014, AAAI.

[7]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

[8]  Raymond Reiter,et al.  The Frame Problem in the Situation Calculus: A Simple Solution (Sometimes) and a Completeness Result for Goal Regression , 1991, Artificial and Mathematical Theory of Computation.

[9]  Wolfram Burgard,et al.  Experiences with an Interactive Museum Tour-Guide Robot , 1999, Artif. Intell..

[10]  Gerhard Lakemeyer,et al.  A Logic for Non-Terminating Golog Programs , 2008, KR.

[11]  Jens Claßen,et al.  Symbolic Verification of Golog Programs with First-Order BDDs , 2018, KR.

[12]  Franz Baader,et al.  LTL over description logic axioms , 2008, TOCL.

[13]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[14]  Eugenia Ternovska,et al.  Non-terminating processes in the situation calculus , 2019, Annals of Mathematics and Artificial Intelligence.

[15]  Craig Boutilier,et al.  Decision-Theoretic, High-Level Agent Programming in the Situation Calculus , 2000, AAAI/IAAI.

[16]  Naiqi Li,et al.  Automatic Verification of Partial Correctness of Golog Programs , 2015, IJCAI.

[17]  Giuseppe De Giacomo,et al.  Verifying ConGolog Programs on Bounded Situation Calculus Theories , 2016, AAAI.

[18]  Scott Sanner,et al.  Practical solution techniques for first-order MDPs , 2009, Artif. Intell..

[19]  Jens Claßen,et al.  Verifying CTL* Properties of GOLOG Programs over Local-Effect Actions , 2014, ECAI.

[20]  Edwin P. D. Pednault,et al.  Synthesizing plans that contain actions with context‐dependent effects 1 , 1988, Comput. Intell..

[21]  Mikhail Soutchanski,et al.  An On-line Decision-Theoretic Golog Interpreter , 2001, IJCAI.

[22]  Carsten Lutz,et al.  Reasoning About Actions Using Description Logics with General TBoxes , 2006, JELIA.

[23]  Werner Nutt,et al.  An Epistemic Operator for Description Logics , 1998, Artif. Intell..

[24]  Franz Baader,et al.  Verifying Properties of Infinite Sequences of Description Logic Actions , 2010, ECAI.

[25]  R. BurchJ.,et al.  Symbolic model checking , 1992 .

[26]  Gerhard Lakemeyer,et al.  Foundations for Knowledge-Based Programs using ES , 2006, KR.

[27]  Franz Baader,et al.  Verification of Golog Programs over Description Logic Actions , 2013, FroCos.

[28]  Jens Claßen,et al.  Decidable Verification of Knowledge-Based Programs over Description Logic Actions with Sensing , 2015, Description Logics.

[29]  Jens Claßen,et al.  Decidable Verification of Golog Programs over Non-Local Effect Actions , 2016, AAAI.

[30]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[31]  Hector J. Levesque,et al.  GOLOG: A Logic Programming Language for Dynamic Domains , 1997, J. Log. Program..

[32]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[33]  Jens Claßen,et al.  Planning and Verification in the agent language Golog , 2013 .

[34]  Joseph Y. Halpern An Analysis of First-Order Logics of Probability , 1989, IJCAI.

[35]  Benjamin Zarrieß,et al.  Complexity of Projection with Stochastic Actions in a Probabilistic Description Logic , 2018, KR.

[36]  Joost-Pieter Katoen,et al.  Discrete-Time Rewards Model-Checked , 2003, FORMATS.

[37]  Jens Claßen,et al.  On the Decidability of Verifying LTL Properties of Golog Programs , 2014, AAAI Spring Symposia.

[38]  Carsten Lutz,et al.  Probabilistic Description Logics for Subjective Uncertainty , 2010, KR.

[39]  Philippe Schnoebelen,et al.  Efficient timed model checking for discrete-time systems , 2006, Theor. Comput. Sci..

[40]  Ray Reiter,et al.  On knowledge-based programming with sensing in the situation calculus , 2001, ACM Trans. Comput. Log..

[41]  Hector J. Levesque,et al.  Tractable Reasoning with Incomplete First-Order Knowledge in Dynamic Systems with Context-Dependent Actions , 2005, IJCAI.

[42]  Gerhard Lakemeyer,et al.  Point-based value iteration: an anytime algorithm for POMDPs , 2003, IJCAI 2003.

[43]  Mikhail Soutchanski,et al.  A description logic based situation calculus , 2010, Annals of Mathematics and Artificial Intelligence.

[44]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[45]  Jens Claßen,et al.  Verification of Knowledge-Based Programs over Description Logic Actions , 2015, IJCAI.

[46]  Hector J. Levesque,et al.  ConGolog, a concurrent programming language based on the situation calculus , 2000, Artif. Intell..

[47]  Gerhard Lakemeyer,et al.  Hybrid Reasoning for Intelligent Systems: A Focus of KR Research in Germany , 2018, AI Mag..

[48]  Fangzhen Lin,et al.  How to Progress a Database , 1997, Artif. Intell..

[49]  Sebastian Junges,et al.  A Storm is Coming: A Modern Probabilistic Model Checker , 2017, CAV.

[50]  Gerhard Lakemeyer,et al.  A semantic characterization of a useful fragment of the situation calculus with knowledge , 2011, Artif. Intell..